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We construct a minimal circuit, based on the top-transmon design, to rotate aqubit formed out of four Majorana zero-modes at the edge of a two-dimensionaltopological insulator. Unlike braiding operations, generic rotations have notopological protection, but they do allow for a full characterization of thecoherence times of the Majorana qubit. The rotation is controlled by variationof the flux through a pair of split Josephson junctions in a Cooper pair box,without any need to adjust gate voltages. The Rabi oscillations of the Majoranaqubit can be monitored via oscillations in the resonance frequency of themicrowave cavity that encloses the Cooper pair box.

Minimal circuit for a flux-controlled Majorana qubit in a quantum spin-Hall insulator